The accuracy of bunching method under optimization
frictions:
Students' constraints
∗
†
Tuomas Kosonen and Tuomas Matikka
November 6, 2015
Abstract
This paper studies how accurately we can estimate the elasticity of taxable
income under the presence of optimization frictions. We especially focus on the
bunching estimator and develop a novel method to investigate to what extent the
local bunching estimator underestimates the global behavioral responses under optimization frictions. We are able to estimate this by utilizing income thresholds
applied to a study subsidy, which all higher education students are eligible for in
Finland. The income thresholds create the notches in the income tax schedule. We
are able to detect the more global eects from the income taxation by utilizing a
reform to the study subsidy rules. We nd that students do respond to incentives
induced by the notches, but at the same time a large fraction of students make
sub-optimal choices by exceeding the income threshold by a small amount. This is
a strong evidence of optimization frictions. By utilizing a reform to study subsidy
rules, we nd that income incentives can aect income in substantial income range.
Although it seems that students in general are aware of the system, we also nd evidence supporting that optimization errors would explain partially the sub-optimal
choices by taxpayers.
Keywords: income taxation, study subsidy, bunching estimator, frictions
JEL Classication Codes: H21, H24, H30
∗
†
Government Institute for Economic Research and CESifo, tuomas.kosonen@vatt.
Government Institute for Economic Research, tuomas.matikka@vatt.
1
1
Introduction
An increasingly active literature utilizes the bunching method to estimate behavioral responses to various tax incentives, following Saez (2010). Kinks in tax schedule sometimes
alter behavior of taxpayers by creating excess bunches in income distributions, and sometimes do not (Bastani and Selin 2014). The modest estimates for the elasticity of taxable
income derived by utilizing the bunching method have been explained by the presence of
optimization frictions (Chetty
et al.
2011). These optimization frictions are collectively
all factors that prevent taxpayers from fully responding to tax incentives according to
standard labor-leisure preferences (Chetty 2012, Kleven and Waseem 2013). Especially
job search costs and other labor market frictions that prevent taxpayers from controlling
their income very precisely could lead to no local behavioral responses to some incentives
(Chetty
et al.
2011). Other kind of frictions are, for example, insucient knowledge
about tax rules and inattention potentially caused by salience of tax regulations (Chetty
et al.
2013, Chetty and Saez 2013, Chetty
et al.
2009).
The bunching method is very local in nature in that it derives the estimate of behavioral response to tax incentives from local excess mass below or around the discontinuity
in incentives. When the incentives are strong enough, such as in the case of notches
(jumps in average tax rates), some behavioral responses are bound to occur. In these
cases the bunching method is capable of answering to the qualitative question, do tax
incentives matter or not. However, the bunching estimator could create biased answer
in the presence of optimization frictions for quantitative question, to what extent tax incentives matter (i.e. elasticity). This bias occurs from the local nature of the estimator.
Kleven and Waseem (2013) developed a correction for local optimization frictions when
calculating the elasticities by taking into account the mass of individuals in dominated
regions, who surely are located there due to optimization frictions. Even this correction
cannot capture the potential global eects of income taxation that aect the income distribution from wider area than around the discontinuous tax incentive. To calculate the
elasticity of taxable income correctly, all behavioral responses due to taxation should be
taken into account.
In this paper we utilize a study subsidy in Finland, which all university students
can apply for (approx. 500 euros/month). We examine the impact of income thresholds
in the study subsidy on income distribution. These income thresholds create notches,
since exceeding an income threshold results in losing one month of study subsidy. The
region above the notch is called the dominated region, and under standard labor-leisure
preferences no one would want to locate themselves there. Thus, the share of individuals
in this dominated region is informative about optimization frictions.
We are able to contribute to the literature in number of ways. First, by utilizing
the local bunching response to income thresholds in the study subsidy, we are able to
2
investigate whether or not taxpayers respond to tax incentives, and by utilizing the
share in dominated region we are able to investigate whether or not this response is
attenuated by optimization frictions. Second, we explore the global nature of responses
to income thresholds by utilizing a reform that shifted out the income thresholds by
about 30%. If the income distribution shifts out with the income thresholds, the total
behavioral response is wider than just the visible bunch and mass in dominated region.
Importantly, the responses beyond these local measures represent the downward bias in
standard bunching estimator when calculating the elasticity of taxable income. These
shifts in income distribution are also informative about overall labor market frictions
that hinder all labor responses to policy shocks. Third, we utilize divided sample results
according to factors that are correlated with optimization abilities in order to separate
out their role in attenuating optimization behavior. This latter analysis is augmented by
utilizing domestic help tax credit, which features a maximum threshold to the credit and
rules that taxpayers potentially misunderstand.
We use register-based panel data on all Finnish taxpayers from 1999-2011. The data
include detailed tax and transfer variables originating from tax- and social administrations. The excellent quality of Nordic administrative data combined with large number of
observations allow us to accurately analyze bunching behavior associated with dierent
kinks and notches, and separate potential bunching behavior from other irregularities in
the income distribution.
Our results shows that taxpayers do respond to tax incentives evident in a visible
bunching behavior below the notch. At the same time it is evident that frictions play
an important role in explaining taxpayer responses to tax incentives. We nd that many
students are located in the dominated region just above the notch. This is compelling
evidence in favor of notable optimization frictions (Kleven and Waseem 2013).
We next turn to understanding the wider scope of income responses to the study
subsidy. We rst investigate how the shape of the income distribution develops over the
years when there is not change in nominal income thresholds. This analysis reveals that
the income distribution for students is rather stable over the years. We then plot the
income distribution for students in two years immediately after the reform. Especially
for students that have the default nine months of study subsidy, the income distribution
shifts out starting from income levels that are far below the income threshold. This
establishes our main result. The behavioral responses to local changes in income tax
incentives turned out to be global in nature. In fact it seems that greater amount of mass
shifted out from bottom part of income distribution than the mass that was bunching
wright below the income distribution. Thus, ignoring total behavioral responses lead
to a severe bias when estimating the elasticity of taxable income by utilizing the local
bunching estimator.
We also nd that although many students increased their income when the income
3
thresholds shifted out in the reform, some also went over the new threshold into the
dominated region. This nding supports the notion that taxpayers do not have precise
control over their income. It seems that students responded to the reform by increasing
their income (by a substantial amount), but could not stop earning at the threshold, and
consequently went over the new income threshold.
Furthermore we nd that the bunch below the previous bunch disappears (and reappears below the new threshold). Thus it seems that students are in general aware of the
fact that the study subsidy eligibility rules have income thresholds.
Despite of this general awareness, it could be that some of the mass in the dominated region could be explained by optimization errors. One source of error is knowledge
about precisely what income concept is used in calculating the income threshold (annual
gross income), and knowledge about which items are considered as income (e.g. holiday
bonuses). We attempted to gain insight into this type of optimization frictions by dividing
students into groups according to how much they have received study credits within the
year. This should be an indication of their abilities to pass exams, or how hard-working
students they are, which both potentially would be positively correlated with how good
they are in understanding details of the rules etc. Interestingly, the results reveal that
the amount of study credits per year is positively correlated with the amount of bunching
and negatively with being in the dominated region.
Finally, we looked into domestic help tax credit utilization to nd support for the
optimization errors result explained above. The domestic help tax credit enables to
deduct certain share (45% or 60% depending on year) of costs of domestic help services
(cleaning and house repairing) up to a maximum amount. A source for optimization errors
is that the guidelines for domestic help credit (from the Tax Administration) highlight
the maximum amount of tax credit, but what needs to be lled in to the tax declaration
is the amount paid for the service. We investigated the share of optimization errors by
plotting the distribution of the declared service use by all taxpayers applying for the
credit. The result shows a clear excess mass around the correct upper limit of service
costs that are deductible, as well as a clear excess mass at the value of maximum tax
credit. This latter excess mass cannot be explained by anything else than the taxpayers
mistook the maximum amount of credit highlighted in the rules to be the maximum
amount of service deductible.
In addition to optimization frictions, this study contributes to the literature on observed responses to kinks and notches (Saez 2010, Bastani and Selin 2014 and Chetty
al.
et
2011). Kleven and Waseem (2013) show that wage earners bunch actively at income
tax notches in Pakistan. We add to this study by estimating responses to income notches
in a developed country where the tax system is strongly enforced, and thus the responses
are more related to labor supply decisions as opposed to reporting behavior. Other existing evidence on responses to notches comes from a range of dierent institutions, for
4
example, the medicaid notch in the US (Yelowitz 1995), eligibility for in-work benets in
the UK (Blundell and Hoynes 2004 and Blundell and Shepard 2012), social security and
nancial incentives in retirement rules (Gruber and Wise 1999 and Manoli and Weber
2011), and car taxes aecting the fuel economy of cars (Sallee and Slemrod 2012).
This paper proceeds by presenting the relevant institutions in Section 2. In Section 3
we present the conceptual background on responding to kinks and notches, and discuss
the role of dierent behavioral frictions. We then present the empirical methodology and
data in Section 4. Section 5 presents the results. Section 6 discusses the implications and
concludes the study.
2
Institutions
2.1
Income taxation and marginal tax rate kink points
We briey study the marginal tax rate (MTR) kink points created by the earned income
tax schedule to be able to compare to other studies on the bunching behavior at kink
points (Saez 2010, Chetty et al. 2011 and Bastani and Selin 2014). The MTR schedule
is nationwide in Finland, and the other local tax schedules are proportional and thus do
not aect the location of kink points.1 Small amounts of earned income are not taxed in
the nationwide schedule, and thus the rst kink appears at a point where the rst tax
rate applies. After this the tax schedule increases in a stepwise manner, which results in
4-6 kink points in MTR, depending on the year in question.
Dierent kink points are associated with MTR increases between 4-11 percentage
points. At the rst income threshold, there is a clear increase in the MTR varying
between 6-14 in percentage points, which relates to a 22-53% decrease in the overall
net-of-tax rate (1-MTR). The last kink involves the most salient and distinctive increase
in the MTR, associated with a 6-9 percentage points increase in the MTR, and 9-16%
decrease in the overall net-of-tax rate.
As an example, Figure 1 presents the marginal income tax rate schedule for the year
2007. The Figure illustrates the discontinuous changes in the income tax rate at dierent
levels of taxable income.
1 The
Finnish income tax system comprises of three components: progressive central government
income taxes, proportional municipal taxes and mandatory social security contributions. The average
municipal income tax rate is 18.3, and the average social security contribution rate is 5.1 (in 1999-2011).
In general, municipal income taxation and social security contributions do not induce kink points since
they are proportional.
5
Marginal income tax rate schedule
.2
.3
Marginal tax rate
.4
.5
.6
Year 2007
0
20000
40000
60000
80000
Taxable income
Note: Marginal tax rates include the average flat municipal tax rate
and average social security contributions
100000
Figure 1: Marginal income tax rate schedule (year 2007)
2.2
Study subsidy
This study focuses on studying discontinuous incentives created by the study subsidy.
In Finland, all students that are enrolled in a university or polytechnic can apply for a
monthly-based study subsidy.2 The maximum amount of the subsidy is 461¿ per month
in the academic year 2006/2007.3 Students can apply for the subsidy for a limited number
of months per degree (max. 55 months).
Students typically rst apply for the study subsidy when they are accepted to a higher
education program. The default number of study subsidy months per academic year is 9
(fall + spring semester), which most students also receive. The study subsidy eligibility
depends on academic progress4 , and on not having too high the yearly gross income
(earned income + capital income) .
The discontinuous incentives are created by income thresholds: if gross income is
higher than the threshold, the study subsidy of one month is reclaimed by the Social
Insurance Institution. Additional month of the subsidy is reclaimed for an additional
2 The
study subsidy is intended to enhance equal opportunities to acquire higher education, and to
provide income support for students who often have low disposable income. In Finland, university education is publicly provided, and consequently there are no tuition fees. A large proportion of individuals
receive higher education in Finland (ca. 40% of individuals aged 25-34 have a degree), and the study
subsidy program is widely used among students.
3 The full study subsidy includes a study grant and housing benet. The standard study grant is
259¿/month and the maximum housing benet is 202¿/month (in 2006/2007). In addition to the study
subsidy, students can apply for repayable student loans which are secured by the central government.
4 The academic progress criteria requires that a student completes a certain number of credit points
per academic year in order to be eligible for the subsidy.
6
1,010¿ of gross income over the threshold. With the typical 9 months of the subsidy
per calendar year, the annual gross income limit is 9,260¿ (in 2006/2007). Students can
alter the number of subsidy months by making an application, or by returning already
granted subsidies by the end of March in the next calendar year. Having more study
subsidy months decreases the income limit.5
Students face large local incentives not to exceed the income limit. Since earning
just a little over the limit results in losing one study subsidy month, this results in an
implied marginal tax rate of over 100% just above the notch. Thus the study subsidy
notch induces a strictly dominated region above the notch where students can earn more
disposable income by decreasing their gross income level.
Disposable income , euros
-400
-300
-200
-100
0
100
200
300
400
Disposable income around the 1st MTR kink
10200 10300 10400 10500 10600 10700 10800
9 months of study subsidy, year 2007
11100 11200 11300 11400 11500 11600 11700
Disposable income, euros
Disposable income around the study subsidy notch
-400
Gross income relative to notch point
-300
-200
-100
0
100
200
300
400
Gross earned income relative to kink point
Figure 2: Disposable income around the study subsidy notch (left-hand side) and the
rst MTR kink point (right-hand side), year 2007
The left-hand side of Figure 2 illustrates the eect of the study subsidy notch on
disposable income with the standard case of 9 study subsidy months (in 2007). In the
gure, the vertical axis denotes disposable income including the subsidy, and the horizontal axis denotes gross income relative to the notch point (9,260¿). The Figure shows
that once the gross income limit is exceeded, reclaiming of the study subsidy causes a dip
in disposable income.
The right-hand side of Figure 2 illustrates the eect of the rst marginal income tax
rate kink point on disposable income. Earning income after the kink point results in less
disposable income than before the kink. For example, 100 euros of gross income above
the kink results in 9 euros less disposable income than below the kink. Figure 2 highlights
that the dierence between the study subsidy notch and the MTR kink points is notable.
The study subsidy program was reformed in 2008. The main outcome of the reform
was that the income limits were increased by approximately 30%. The default income
limit for 9 study subsidy months increased from 9,260¿ to 12,070¿6 In addition, the
formula for the annual gross income limit is the following: 505¿ per study subsidy month plus
a xed amount of 170¿, and 1,515¿ per month without the study subsidy (in 2006/2007).
6 After 2008, the gross income limits are 660¿ (before 505¿) per study subsidy month plus a xed
5 The
7
monthly study subsidy was increased from 461¿ to 500¿ per month. In general, other
details of the system were not changed, including the academic criteria and the loss of the
subsidy of one month if the income limit is exceeded.7 Finally, Table 2 in the Appendix
shows the income limits for dierent number of study subsidy months, and the relative
loss incurring when the income limit is exceeded both before and after the reform.
3
Conceptual framework
We analyze taxpayer responses to kinks and notches in the tax schedule in the lines of Saez
(2010) and Kleven and Waseem (2013). We are in particular focusing on understanding
the role and type of optimization frictions, and thus focus on analyzing the responses to
notch point created by the study subsidy. In general both kinks and notches could create
behavioral responses, kinks typically smaller than notches, in the form of some individuals
bunching at or below the discontinuous point in the tax schedule. The distinction between
these is that notches create a dominated region where it is clearly not optimal to locate,
and if taxpayers still locate there, it is a sign of optimization frictions. Kinks do not have
that feature.
We follow the bunching literature in utilizing discontinuous incentives in tax schedules
and analyzing their eects from excess mass around these discontinuities. In the literature more excess mass relative to some counterfactual means larger behavioral responses
which in turn, given the size of change in incentives, leads to a larger elasticity estimate.
Comparative statics are then possible by comparing the relative sizes of excess masses
across dierent subgroups. However, for the elasticity calculation the optimization frictions create complications, because they potentially aect the counterfactual distribution.
Kleven and Waseem (2013) correct for the optimization frictions by adding to the excess
mass the share in the dominated region. This correction is only possible for notches, and
it is local in nature. If some frictions aect the shape of the income distribution more
generally, this correction still underestimates the extent of behavioral responses, and thus
the size of the elasticity of earned income (since the size of incentives is known, and thus
xed). We attempt to utilize dierent reference groups and the reform in 2008 to build
more global counterfactual for the shape of the income distribution without the study
subsidy income thresholds.
In the analysis, we decompose behavioral frictions into two broadly dened components: inability to respond to tax incentives and optimization errors. The former category
is thought to arise from frictions in the labor markets, and in that sense not directly under
amount of 220¿ (170¿), and 1,970¿ (1,515¿) per month when no study subsidies are collected.
7 After 2008, additional month of the subsidy is reclaimed for an additional 1,310¿ of gross income
over the threshold, compared to 1,010¿ before 2008.
8
the control of the individual. The latter category is to some extent under the control of
the taxpayers, in that they could pay more attention to understanding tax incentives.
The inability to respond covers a range of reasons why taxpayers are not able to
exibly respond to tax incentives. The inability to respond might stem from constraints
to optimization. For example, due to non continuous wage-hour employment contracts,
wage earners might not be able to alter their working hours easily. Especially those
working part-time (including university students) may receive work oers for December
that they could not predict, and declining them would lead to losing the whole job
contract. Due to the large incentives created by the notch in the study subsidy, students
may decide not to work at all during the winter for the reason that they expect this extra
part time work resulting in the going over the income threshold and consequently losing
subsidies. Also, it might be costly to search for a new job that provides more suitable
working hours and wage rates in terms of tax incentives (see e.g. Chetty
et al.
2011 and
Chetty 2012).
Optimization errors include complete unawareness of tax rules, errors in understanding
all relevant income and tax concepts (i.e. confusing marginal and average tax rates) and
ability to calculate an optimal response to incentives (see e.g. Chetty and Saez 2013, and
Liebmann and Zeckhauser 2004). Students are likely to be, at least at some level, aware of
the income thresholds in the study subsidy, since they are clearly stated in the application
form and guidelines describing the system. However, it could be possible that students
don't always understand the exact income denition (gross earned plus capital income)
used to dene the income threshold in the study subsidy, or which income items are
taken into consideration. One example are the (completely predictable and deterministic
part of wage income) holiday bonus salaries, that students may forget to include when
calculating their annual gross income.
We attempt to shed light on the signicance of ability to control income by examining the behavioral responses to the reform that changed shifted the income threshold
out. The reform to study subsidy helps us to discover whether or not the responses to
taxation are limited to the local responses. We can measure the total mass of taxpayers
that increase their income in response to shifting out of the earnings thresholds. If the
income distribution shifts out due to the reform, it indicates that the total responses are
greater than those measured by the bunching behavior. We can also build alternative
counterfactual distributions from subgroups that resemble students in their labor market
behavior, but are not applying for the study subsidy, and thus not subject to the income
incentives it creates. Whenever we nd that study subsidy aects the global shape of
income distribution, it reveals that ability to control income inuences behavior. This is
because the optimization errors type of frictions should lead to more local attenuation,
like exceeding the income threshold by a small amount, whereas ability to control income
potentially aect income in a large income span.
9
We also investigate if the optimization errors by a role in attenuation optimization
behavior by studying the share of individuals in the dominated region across subgroups
and to what extent people are aware of the shifting out of the income thresholds. It would
be especially revealing if some students would continue bunching at the old thresholds,
and if not, would indicate that they are at least aware of the overall system. For subsamples we look at factors that are potentially correlated with optimization ability. One
such factor are study credits, basically how many courses were passed during the year.
Low number of study credits could be correlated with low ability and vice versa. Thus
dividing results into high and low study credits allow us to look at how optimization
errors are correlated with optimization behavior. Other things correlated with ability
could be majors in universities where it is more dicult to get in versus easy to get into
places. As a supplementary results supporting the optimization errors mechanisms we
look at the domestic help tax credit utilization and to what extent that reects taxpayers
not fully understanding the rules of the tax credit.
Another division of results related to understanding how to optimize within the study
subsidy system is how long a student has been a student. If bunching is greater for
students that have been longer time in the system, it indicates that learning how to
optimize played a role in behavioral responses. On the other hand, if time spent in the
system has no eect to the results, it would indicate that learning or any diculty to
understand the optimization of income plays no role. Similarly, if time spent in the study
subsidy system has any correlation for the share of students in the dominated region,
optimization frictions could arise partly because students at rst did not know how to
optimize and avoid the dominated region, and learned that later on.
4
Data
We use panel data on all working-aged individuals (15-70 years) living in Finland in
1999-2011. The data set is based on the Finnish Longitudinal Employer-Employee Data
(FLEED). To this data we have linked a variety of essential register-based variables,
such as detailed tax register data from 1999-2011, and information on students and the
study subsidy program from 1999-2010. With this data we can reliably and accurately
analyze local changes in incentives among various subgroups of taxpayers. To analyze
self-employed individuals, we use panel data on all main owners of Finnish businesses
from 1999-2010, provided by the Finnish Tax Administration.
Table 3 in the Appendix presents the key summary statistics for all taxpayers. Table
4 shows the summary statistics for students. The average gross income excluding the
study subsidy among students is 7,600 euros per year. This implies that many students
have part-time or full-time jobs during their studies and breaks between semesters, which
is very typical among Finnish university students. Finally, Table 5 presents the summary
10
statistics for the self-employed individuals, including the key rm-level characteristics.
5
Results
5.1
Baseline results
This section presents the overall results on bunching at MTR kink points and the study
subsidy notch. We characterize the role and signicance of frictions in the following
sections.
Marginal tax rate kink points
First, we present taxable income distributions around
dierent MTR kink points for all taxpayers. The gures plot the observed income distributions and counterfactual distributions relative to each MTR kink point in bins of 100¿
in the range of +/- 5000¿ from the kink. The gures denote the excess mass estimates
(with standard errors), and the implied elasticity estimates based on observed excess
bunching.
In each graph, the kink point is marked with a dashed vertical line. The excluded
counterfactual region (the bunching window) is marked with solid vertical lines. In each
graph, the bunching window is +/- 7 bins from the kink. The counterfactual density
is estimated using a 7th-order polynomial function. Our results are not sensitive to the
choice of the bunching window and the order of the polynomial.
Figure 3 presents the income distributions around dierent kink points of the MTR
schedule for all taxpayers. The gure illustrates bunching at the rst, second, third and
last kink point using pooled data for the years 1999-2011. As shown in Table 1 in the
Appendix, the number of kink points have decreased from 6 to 4 in the period we study.
Throughout the study, the rst MTR kink point always includes the threshold where the
national income tax rate rst applies. The other kink points in Figure 3 correspond to
the kink points still existing after 2007.
The Figure shows that there is no bunching at the marginal tax rate kink points in
Finland. The only conceivable exception might be the second kink. However, the second
kink is likely to produce upward-biased excess bunching because of the locally hollow
shape of the income distribution around the kink. Consequently, the elasticity estimates
are zero or very close to zero at all MTR kink points.
The result of no bunching at MTR kink points in gure 3 indicates that marginal tax
rates do not induce local behavioral responses. This could be explained by both the low
underlying (local) tax elasticity and various behavioral frictions. Small elasticities would
mean that the relatively small changes in incentives do not induce behavioral responses,
even in the absence of frictions and even modest optimization frictions would prevent
taxpayers to react to kink points even if they would want to do so. Unfortunately, with
11
Second MTR kink, all taxpayers
Frequency
95000 100000 105000
Frequency
50000 60000 70000 80000 90000 100000
First MTR kink, all taxpayers
Excess mass: .095 (.035), Elasticity: .004(.001)
85000
90000
Excess mass: -.048 (.076), Elasticity: -.003(.005)
-40
-30
-20
-10
0
10
Distance from the kink
30
40
50
-50
-40
-30
Counterfactual
-20
-10
0
10
Distance from the kink
Observed
20
30
40
50
40
50
Counterfactual
Third MTR kink, all taxpayers
Last MTR kink, all taxpayers
Excess mass: .01 (.023), Elasticity: 0(.001)
Excess mass: .005 (.065), Elasticity: 0(.001)
4000
5000
Frequency
6000 7000
8000
Frequency
40000 50000 60000 70000 80000 90000
Observed
20
9000
-50
-50
-40
-30
-20
-10
0
10
Distance from the kink
Observed
20
30
40
50
-50
Counterfactual
-40
-30
-20
-10
0
10
Distance from the kink
Observed
20
30
Counterfactual
Figure 3: Income distributions around MTR kink points, 1999-2011
the no bunching anywhere results we cannot separate whether it is about elasticities or
frictions, and if the latter, what kind of frictions. Thus we turn to analyzing the study
subsidy notches, since they create larger incentives and allow to gauge into the existence
and source of optimization frictions.
Study subsidy notch
Next, we study behavioral responses around the notch points
of the study subsidy system among Finnish university students. Figure 4 shows the
gross income distribution around the notch point (relative to the notch in bins of 100¿
in the range of +/- 5000¿ from the notch). The gure presents the distribution of all
students (left-hand side) and students with the default number of 9 study subsidy months
(right-hand side) in 1999-2010. In the gure, the dashed vertical line denotes the notch
point above which a student loses one month of the subsidy. The solid vertical lines
denote the excluded range (see Section 4 for details on dening the upper limit of the
excluded range). The dash-point vertical line above the notch shows the upper limit for
the dominated region.
The gure also includes the estimates and standard errors for the excess mass at
the notch, the share of individuals in the dominated region, and the upper limit of the
counterfactual and ∆z . In each gure the counterfactual density is estimated using
12
a 7th-order polynomial function. Our main conclusions are not very sensitive to this
choice, although the point estimates vary somewhat with dierent choices on the degree
of polynomial.
Study subsidy notch, all students
Study subsidy notch, students with default subsidy (9 months)
6000
Excess mass: 1.903 (.269), Share in the dominated region: .881 (.039)
Upper limit: 23 (3.24)
0
2000
4000
Frequency
2000
4000
Frequency
6000 8000 10000 12000
Excess mass: 2.046 (.227), Share in the dominated region: .906 (.032)
Upper limit: 26 (4.613)
-50
-40
-30
-20
-10
0
10
20
Distance from the notch
Observed
30
40
50
-50
Counterfactual
-40
-30
-20
-10
0
10
20
Distance from the notch
Observed
30
40
50
Counterfactual
Figure 4: Bunching at the study subsidy notch, 1999-2010
Figure 4 indicates a clear and statistically signicant excess mass on the left of the
notch for both all students (1.8) and students with the default subsidy (2.0). This indicates that students are both aware of the notch and respond to the strong incentives
created by it. However, these responses are not large compared to the large incentives. To
have some understanding on the size of elasticities, we calculated them using Kleven and
Waseem (2013) reduced form method (not taking optimization frictions into account).
The implied earnings elasticities are 0.083 (0.019) for all students and 0.065 (0.007) for
students with 9 subsidy months (standard errors in parenthesis).8 Thus even though
excess bunching is evident and notable earnings responses occur (4z is around 15% of
disposable income at the notch), the observed elasticities are still small. This stems from
the fact the changes in incentives are also very distinctive, as notches induce very high
implicit marginal tax rates above the income limit.9
Figure 4 implies that students are aware of the incentives and respond to the notch
created by the income limit of the study subsidy program. However, the gure also shows
clear evidence on the existence of optimization frictions. There is an economically and
statistically signicant mass of students at the strictly dominated region above the notch
where students can increase their net income by lowering their gross income. It should
8 Earnings
elasticity for all students is calculated using the average number of study subsidy months
(7). All elasticities at study subsidy notches are calculated using the SISU microsimulation model and the
average number of subsidy months. We thank Markus Paasiniemi for research assistance on calculating
the elasticities.
9 In addition, implicit marginal tax rates remain relatively high (>50%) even further away above the
notch, as an extra month of the subsidy is reclaimed after additional 1,010¿ above the income limit
(1,310¿ after 2008). Thus, the eective tax schedule for students inherently includes multiple notches.
However, we only observe signicant bunching at the rst notch, which justies the analysis of the rst
notch only. The analysis of the rst notch is also rationalized by the fact that students can alter the
number of study subsidy months until the march of next tax year.
13
be highlighted that under no standard model of economic behavior would no one want
to be located in the dominated region, it is clearly sub-optimal. There is 80-90% of the
mass compared to the counterfactual in the region where students would save money
by earning less. Thus, this is clear evidence of a very signicant optimization friction.
Despite of that, it still does not tell us what is the source of the friction, whether it is that
students do not know exactly how to calculate their income used to dene the income
thresholds, or that they would like to locate below the threshold but something prevents
them.
Next, we compare the responses of students around the study subsidy notch and
the MTR kink points. There is a striking dierence between bunching at notches and
bunching at MTR kinks. Figure 5 shows income distributions around MTR kink points for
current students (rst kink), university graduates (last kink) and students who previously
bunched at the study subsidy notch (rst kink). For all of these groups we nd no
signicant bunching at any MTR kink point in any year.
Even though students are clearly responding to large incentives induced by the notch,
they do not respond to smaller incentives created by MTR kinks. For current students
this cannot be explained by the inability to respond to
any
local incentives, as we observe
similar or even the same individuals bunching at income notches. In other words, there is
no fundamental reason to assume that students are less able to aect their labor supply
around the MTR kink compared to the study subsidy notch. Nevertheless, this result
does not indicate that students would not respond to MTR kinks of
any
size. Larger
changes in the MTR might induce larger observed behavioral responses, as with larger
kinks it becomes more protable to adjust labor supply (see Chetty
et al.
2011, and
Chetty 2012). However, in addition to the size of the incentive, the underlying elasticity
and the inability frictions, it might be that the MTR schedule is too obscure for many
students.
5.2
Local versus global focus
Above we zoomed in the notches created by study subsidies and found that they create
local responses in income distribution. This type of analysis is in the very hart of the
bunching method, looking at local eects created by local incentives. However, the rst
indication that not all the results are completely local is that the excess mass is fairly
diuse in Figure 4. That observation raises the question that to what extent the strong
incentives created by the study subsidy income thresholds aect the shape of the income
distribution more globally.
To have a rst look at the shape of income distributions, Figure 6 plots the income
distribution for students and non-students that are young part-time workers. The idea
of the latter group is to serve as a rst version of counterfactual distribution for students
14
Last MTR kink, university/polytechnic graduates
Excess mass: -.106 (.084), Elasticity: -.001(.001)
2500
3000
Frequency
3500 4000
4500
5000
Frequency
5000 10000 15000 20000 25000 30000
First MTR kink, all students
Excess mass: -.09 (.107), Elasticity: -.006(.007)
-50
-40
-30
-20
-10
0
10
Distance from the kink
Observed
20
30
40
50
-50
-40
-30
Counterfactual
-20
-10
0
10
Distance from the kink
Observed
20
30
40
50
Counterfactual
First MTR kink, students who previously bunch at the notch
1000
Frequency
2000
3000
4000
Excess mass: -.656 (.183), Elasticity: -.044(.012)
-50
-40
-30
-20
-10
0
10
Distance from the kink
Observed
20
30
40
50
Counterfactual
Figure 5: Bunching at MTR kink points: Current students, graduates and students who
bunched at the study subsidy notch, 1999-2010
without any income thresholds. Since students need to spend time on studying, they
empirically seem to have quite often part-time jobs (in work less than 12 months a year)
and students tend to be young as well. Thus, we selected from a group of non-students
a subgroup that match these characteristics: individuals who have less than 12 months
in working contracts per year and who are between 19 to 30 years old.
The resulting income distributions show intriguing patterns in Figure6. Both groups
have declining pattern to the right and most of the mass in distribution is in roughly
similar income intervals. The dierences in shapes are interesting, students have a peak
at low income levels, which could be explained by students not wanting to cross the
income threshold. Also, there is signicantly less mass at higher income levels, at higher
income levels than most thresholds. Non-students do not feature these anomalies in the
shape of distribution, which is steadily declining.
To have a clearer view on the role of income thresholds we repeat the exercise for
students that have 9 study subsidy months per year. Prior to the reform in 2008 their
income threshold is at 9620 euros. We took a bit more focused age restriction to match
this group of students; non-students that are part-time workers and between 10 and 24
years of age. Figure 7 shows the resulting distributions. The income distribution for
students show that most want to stay below the income threshold and there is relatively
15
Income distributions for students and non−students
15000
0
0
Non−students
5000
10000
5000
10000
Students
15000
Non−students: part−time workers, aged 19−30
1500
4500
7500
10500
Income
Students
13500
16500
19500
Non−students
Figure 6: Income distributions for students and non-student part time workers
thin mass above it. The distribution for non-students continues to be smooth and steadily
declining around the notch.
This analysis points out that perhaps all the responses that the notches create are not
just the local bunching behavior. It is conceivable that notches have more global eects
especially if taxpayers do not have precise control over their income. We next turn to
analyzing the eect of the reform in 2008 on the whole income distribution to have a
more precise look at these global eects.
5.3
Utilizing the reform to understand the sources of optimization frictions
Based on the result that there are signicant share of students in the dominated region,
we established that optimization frictions signicantly attenuate optimization behavior.
That result by itself does not allow us to gauge into the underlying reasons for optimization frictions. Next we look into the eects created by the reform to study subsidy rules.
The details are discussed in the institutions section, but the essence of the reform is that
it shifted out the income thresholds by about 30%; with the same level of subsidies a
student can now earn more before hitting the notch.
We rst look at the income distribution of students across the years without focusing
on the surrounding of any notch or conning to specic amount of study subsidies. We
group always two years together to have more observations, and look how the income
distribution develops from 2004 and 2005 to 2006 and 2007 before the reform and then
16
Income distributions for students and non−students
0
1000
1500
3000
4500
Students
Non−students
2500
4000
5500
6000
7000
Students: 9 subsidy months
Non−students: part−time workers, aged 19−24
1500
4500
7500
Students
10500
Income
13500
16500
19500
Non−students
Figure 7: Income distributions for students with 9 study subsidy months and non-student
part time workers
to 2008 and 2009 after the reform. We plot the kernel densities for dierent years in the
same graph to facilitate the visual comparison of income distributions. Graph 8 presents
the results. From the graph it is clear that the overall shape of the distributions are
similar, especially in the higher income range. It also seems that substantial amount of
income has shifted out from the bottom end of distribution after the reform in 2008.
To have a more close look at the eect of study subsidy on earned income, we focus
on students that have 9 months of subsidy before and after the reform. This group have
the same level of subsidies before and after, and the only thing that changes is the ability
to earn more income before the subsidies are withdrawn. Thus we focus on the eect
of incentives on earnings behavior and hold other factors constant. Graph 9 shows the
results. The distributions in the years before the reforms develop similarly to each other,
at least close to the threshold. This gives an idea how the distribution would evolve
without the reform. The post-reform distribution in the dotted line shows drastically
dierent shape. The bunch below the previous income threshold has disappeared and
a new smaller bunch has appeared below the new income threshold. More generally,
income distribution has shifted everywhere to the right. This is a remarkable result and
highlights that the income threshold had larger eect on incomes than just the local
bunching eect, otherwise the mass in the income distribution had not shifted up from
such a wide range.
Another interesting point about the eect of the reform on the shape of the income
distribution is that mass has shifted up also beyond the income threshold into the new
17
Income distribution in different years
0
Frequency
1000 2000 3000 4000 5000
All students
0
5000
10000
Income
2004−2005
2008−2009
15000
20000
2006−2007
Figure 8: Income distribution for all students before and after the reform
dominated region. This tells us something interesting about the optimization frictions;
individuals aim to be located in the range below the new threshold, but something pushes
them above it. This together with the fact that the bunch disappeared from the old
threshold is a strong indicator that individuals are in general aware if the system, but
they either cannot calculate correct income to stay below threshold accurately, or they
face unpredictable shock pushing them over the threshold, potentially coming from the
labor markets. Overall the fact that the shifting out of the income threshold in the reform
had an eect in such a wide range of incomes indicates that taxpayers have diculty to
control their income precisely. The result suggests that some stay below quite far below
the threshold for the fear that if they try to increase their income to the next possible
level, they would go over the threshold.
We next utilize the reform in a dierent way to try to understand whether students
sometimes fail to optimize on their own accord despite of being generally aware of the
system and thresholds. We do this by dividing students into new students and students
who have already spent some time in the system and also by dividing rules to old rules,
which have been in eect for a number of years, and new rules, which have been in
eect only for a year or two. This distinction is meaningful, since for new students
understanding how to optimize perfectly the fact whether rules are new or old should
not matter, they are new to the student regardless. On the other hand, old students
should already have had more time to learn how to optimize, but they may have frictions
coming from the labor market preventing them to adjust their income level immediately.
For example, they would need to switch jobs in order to adjust income, and nding a
18
Income distribution in different years
0
Frequency
200
400
600
Students with 9 subsidy months and 9 subsidy months in base year
0
5000
10000
Income
2004−2005
2008−2009
15000
20000
2006−2007
Figure 9: Bunching at the study subsidy notch for those having 9 subsidy months before
and after the reform
new job requires overcoming search costs.
Graph 10 presents the bunching and dominated regions for new and old students
and rules. The result is that both frictions nd support, inability to adjust income and
unawareness of how to optimize exactly. The most remarkable result is found by comparing new students under the old and new rules. New students feature quite signicantly
less bunching under the new rules. This is intriguing, since new students close to the
threshold should want to optimize and stay below the threshold, and act according to
rules they get from Social administration. Since they don not do this, it seems they had
been getting instructions on how to optimize from the network of peers and more senior
students. With the new rules this information is not accurate anymore, since it applies
to the old rules, like what the more senior students or siblings did last year.
The graph also shows that older students feature less bunching under the new rules.
Given that they managed to optimize before, they should know how to optimize. The
fact that they optimize by bunching close and below the threshold less often points to
the direction that some of them had dicult time adjusting their income upwards with
the threshold. Finally, there is no signicant dierence in the share of taxpayers in the
dominated region. This is somewhat puzzling, but could be explained by precisely the
inability to control income exactly, which results for many taxpayers to being located
in the dominated region. If the only optimization friction would be about failure to
optimize, this would be visible in the old and new students graphs as dierent shares in
the dominated region.
19
Study subsidy notch, new students after the reform
0
500
500
Frequency
1000
Frequency
1000
1500
2000
1500
Study subsidy notch, new students before the reform
−50
−40
−30
−20
−10
0
10
20
Distance from the notch
30
40
50
−50
−40
−20
−10
0
10
20
Distance from the notch
30
40
50
40
50
Study subsidy notch, old students after the reform
200
500
400
Frequency
600
800
Frequency
1000
1500
1000
2000
1200
Study subsidy notch, old students before the reform
−30
−50
−40
−30
−20
−10
0
10
20
Distance from the notch
30
40
50
−50
−40
−30
−20
−10
0
10
20
Distance from the notch
30
Figure 10: Bunching at the study subsidy notch: results divided into old and new students
and rules
To characterize the eect of the change in the income limit due to the reform even
more closely, we take students with any number of subsidy months and who were located
in the bunching region in the pre-reform period and look at their behavior after the
reform. Figure 11 shows that these students also bunch actively after the reform. The
observed earnings elasticity at the notch for this group is 0.067 (0.027). Since those
having optimized before are more like to do so under the new rules indicates that there
is something individual specic about the ability to optimize. However, since a large
number of students are located in the dominated region above the notch, it seems that
inability to adjust real labor supply causes optimization to be imperfect even for students
who have demonstrated earlier that they are active optimizers.
5.4
Utilizing divided sample results
We have established that inability to control labor income perfectly as well as failure to
optimize seem both to explain average attenuation bias of optimization behavior. Since it
may be important to know which one is more prominent, we provide some divided sample
results to gain more insight into this. We divide the sample of universe of students in
20
100
200
Frequency
300
400
500
Study subsidy notch, students who bunched before the reform
−50
−40
−30
−20
−10
0
10
20
Distance from the notch
30
40
50
Figure 11: Bunching at the study subsidy notch: Students who bunched before the reform
(2005-2007), 2008-2010
a way that is likely to be correlated in an interesting way with the general ability to
optimize.
We rst divide students according to their study credits per academic year. We think
that student achievements are indications of general intellectual properties of a student
(at least on average), or how hard working they are. Both are likely to result, on average,
that higher study credit scores should be able to optimize according to rules, but not
so much how the labor market works. Thus, if the study credits have any bearing on
the bunching behavior, it is likely to be caused by personal optimization abilities of the
student rather than inability to control labor market income due to labor market frictions.
Graph 12 presents the results, where students are divided into four bins according to
their study credits. The results show clearly that higher study credits are both positively
correlated with amount of excess mass in the bunching region and negatively with the
share in dominated region. This is a remarkable result, since not only it shows that
optimization ability drives some of the bunching behavior, but also this is the rst result
where we got some dierence between groups for the share in the dominated region.
The result suggests that higher ability students are less likely to make the mistake of
calculating their income incorrectly and thus resulting to be located in the dominated
region. Thus, although inability to control income seems quite predominant explanation
according to the previous results, some of the optimization frictions is also explained by
unawareness of the details of the rules or ability to adjust own behavior according to
them.
We also attempted to nd support for this result by dividing majors into how presti-
21
500
Frequency
1000
1500
Study subsidy notch, study credits 25−50th percentile
0
0
500
Frequency
1000
1500
Study subsidy notch, study credits 25−50th percentile
−50
−40
−30
−20
−10
0
10
20
Distance from the notch
30
40
50
−40
−30
−20
−10
0
10
20
Distance from the notch
30
40
50
2500
Study subsidy notch, study credits 75−100th percentile
0
0
500
500
Frequency
1000
1500
Frequency
1000
1500
2000
2000
2500
Study subsidy notch, study credits 50−75th percentile
−50
−50
−40
−30
−20
−10
0
10
20
Distance from the notch
30
40
50
−50
−40
−30
−20
−10
0
10
20
Distance from the notch
30
40
Figure 12: Bunching at the study subsidy notch: results divided according to study
credits achieved
gious they are. For more prestigious a student needs higher score from both matriculation
and intake exam to get in, and this would be correlated with intellectual properties of
the student. Since scores are based on university specic majors, we can divide students
according to their major and university and in this way overcome spurious correlations
coming from specic cities or majors. This is work in progress, but tentative results
support the hypothesis coming form the study credit scores.
The results utilizing the reform suggested that students have imprecise control over
their income. This raises the question of the relationship between the amount of working
and bunching behavior. It would be natural to think that students who are close to
the income thresholds also work somewhat, to have enough income to be close to the
threshold. To analyze this, we divided students into two groups, those that have less
than 10 months employed and to those that have 10 or more months. Figure 13 shows
the resulting distributions. Strikingly, almost all of the bunching behavior comes from
students that have 10 or more months as employed whereas those that work less months
have substantially more mass at the lower part of income distribution. This divided
sample result gives support to the result that students who respond to the incentives
22
50
work in most months. Therefore it is also credible to think that they could have low
degree of control to their precise income, originating from decisions like should I work
one month more or not.
Income distribution for students, 2001−2010
0
1000
Frequency
2000
3000
4000
Students with different number of months employed
1500
4500
7500
10500
Income
> 10 months employed
13500
16500
19500
< 10 months employed
Figure 13: Students' income distribution divided by 10 months employed
To further study to what extent students are aware of the study subsidy rules, we
look at students who previously located themselves in the dominated region just above
the notch. In this region, students could earn more disposable income by earning less
gross income. In addition, students who exceed the income limit receive a letter from the
Social Security Institution which states that (at least) one month of the subsidy needs
to be paid back (with 15% interest). Thus for the students who are just over the income
limit, there are both large incentives to adjust behavior in the future as well as increased
awareness of the incentives and the existence of the income limit due to the received
letter.
Figure 13 shows the income distribution around the notch for those students who were
located in the dominated region in any of the three previous years. Figure shows that
students bunch actively at the notch after locating in the dominated region before. The
elasticity estimate at the notch for this group is 0.112 (0.051). However, a notable share
of individuals still fail to optimize and are located in the dominated region also in future
years. This suggests that inability to respond largely matters even with large incentives
and when awareness is generally increased. However, the non-monotonic shape of the
income distribution around the notch for this particular group induces notable variation
in the estimates, which thus need to be interpreted with caution.
23
Study subsidy notch, students in the dominated region before
200
Frequency
400
600
800
Excess mass: 2.16 (3.185), Share in the dominated region: .940 (.202)
Upper limit: 32 (10.112)
-50
-40
-30
-20
-10
0
10
20
Distance from the notch
Observed
30
40
50
Counterfactual
Figure 14: Bunching at the study subsidy notch: Students who were in previous years in
the dominated region (t − 1, t − 2 or t − 3,), 1999-2010
5.5
Domestic help tax credit
Above we established that optimization errors seem to explain part of the mass at the
dominated region in the study subsidy. To nd support for this result from elsewhere in
the tax system, we look at the use of domestic help tax credit. It is quite generous tax
incentive in Finland to support demand for rms that provide domestic help services,
mainly cleaning and house repairing.
The general rules in the domestic help tax credit are that there is a certain percentage
of the value of the service used that is deductible directly from income taxes. The credit
has a maximum amount which together with the replacement percentage dene maximum
value of the service that is deductible. The rules have changed over the years; 20092011 60% of the value of service was deductible until 3000euros maximum amount and
2012-2013 45% of service was deductible until maximum of 2000euros. These limits and
percentage give about 5167euros and 4667euros for the maximum value of services used,
respectively.
A source for confusion in the guidelines given by the Tax Administration is that the
maximum amount of tax credit is very prominently highlighted, but when it comes to
the tax declaration form, the actual value of service needs to be lled in. If taxpayers
wanting to deduct the tax credit do not read the instructions carefully, they may ll in
the value of tax credit instead of value of service. If this occurs, they will lose disposable
income, since the amount of credit is smaller (by the deduction percentage) than the
24
0
.005
Fraction
.01
.015
.02
.025
Total costs in Domestic help credit, years 2009−2011
0
1000
2000
3000
4000
5000
Total costs in domestic help credit, eur
6000
0
.005
Fraction
.01
.015
.02
Total costs in Domestic help credit, years 2012−2013
0
1000
2000
3000
4000
Total costs in domestic help credit, eur
5000
6000
Figure 15: Value of services in domestic help tax credit in dierent years
value of service.
Figure 15 shows the value of services for all taxpayers that claimed the domestic help
tax credit in dierent years. Both panels in the Figure show that the is a spike and
also diuse excess mass at and around the maximum value of service that leads to a
maximum tax credit. Interestingly, the Figure also shows that there is a second spike
that corresponds the maximum amount of tax credit. These can only be due to errors,
taxpayers mistook the item in tax declaration form to be amount of tax credit applied
instead of the value of the service, which it actually is. This result conrms that taxpayers
do optimization errors that cost them substantial amount of income.
25
6
Implications and conclusions
We nd that students bunch actively at the income notch induced by a study subsidy.
At the same time we nd that signicant share of students are located in the dominated
region, where they strictly lose disposable income relative to earning less. This is a strong
indication of optimization frictions.
To better gauge at exactly how large behavioral eects the income thresholds in
the study subsidy create, we look into the eects of the reform that shifted out the
income thresholds. The results indicate that students seem to be in general aware of
the system, but they still often exceed the income thresholds, that the study subsidy
creates larger eects that visible just by looking at the amount of bunching. This is
important nding in terms of both calculating the size of the income elasticity correctly,
and also as a methodological contribution. By utilizing sharp changes in local incentives
one can observe whether or not the incentives create some responses, but in the presence
of optimization frictions it is possible that one cannot straightforwardly calculate the size
of the elasticity from the local behavioral response (Kleven and Waseem 2013).
We also divide students into subgroups that are correlated with interesting factors in
terms of optimization behavior. Students who earn more study credits during academic
year ought to be able to optimize according to study subsidy rules better. Interestingly our
results point out that those having higher credits also bunch below the income threshold
more often and are located in the dominated region less often. Supporting evidence for
this is that taxpayers sometimes make costly mistakes when claiming domestic help tax
credits. The second interesting exercise we do is to divide students into new and old,
and look at their behavior when rules have been place form many years and when they
have just been reformed. The intriguing result is that new students bunch signicantly
less under the new rules than under the old rules. Since for new students are new to
the rules, it should not matter whether the rules have recently changed or not. Since
it does matter, it seems that new students need tutoring from more senior students in
order to be able to optimize correctly, and that under the new rules senior students do
not themselves know how to optimize that well.
Understanding the role of dierent optimization frictions has important policy implications. It is important to understand whether they attenuate very local behavior or
optimization in more broad terms. The former has more limited eect on government
tax revenue than the latter. Dierent frictions might also imply dierent patterns of responding to similar tax incentives (Reck 2014, Chetty et al. 2009 and 2007). For example,
when observed behavioral responses are attenuated by the inability to respond immediately because of rigid labor demand, we would expect individuals to adjust their behavior
in the future, and this adjustment might cause notable welfare losses. In contrast, when
responses are attenuated by unawareness of tax regulations or inattention, it is not clear
26
whether individuals would be more aware or attentive over longer time (and change their
behavior accordingly). Then individuals would continue to be in sub-optimal choice for
themselves, but it would have more limited eect on government tax revenue.
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28
Appendix
Year
Taxable income (in euros)
Marginal tax rate
Year
Taxable income (in euros)
Marginal tax rate
1999
7,905-10,596
5,5
2005
12,000-15,400
10,5
10,596-13,455
15,5
15,400-20,500
15
13,455-18,837
19,5
20,500-32,100
20,5
18,837-29,601
25,5
32,100-56,900
26,5
29,601-52,466
31,5
56,900-
33,5
52,461-
38
12,200-17,000
9
2000
2001
2002
2003
2004
2006
8,006-10,697
5
17,000-20,000
14
10,697-13,623
15
20,000-32,800
19,5
13,623-19,005
19
32,800-58,200
25
19,005-29,937
25
29,937-52,979
31
2007
58,200-
32,5
12,400-20,400
9
52,979-
37,5
20,400-33,400
19,5
11,100-14,296
14
33,400-60,800
24
14,296-19,678
18
60,800 -
32
19,678-30,947
24
12,600-20,800
8,5
30,947-54,661
30
20,800-34,000
19,0
54,661-
37
34,000-62,000
23,5
11,500-14,300
13
14,300-19,700
17
19,700-30,900
30,900-54,700
2008
62,000 -
31,5
13,100-21,700
7
23
21,700-35,300
18
29
35,300-64,500
24
54,700-
36
64,500 -
30,5
11,600-14,400
12
15,200-22,600
6,5
14,400-20,000
16
22,600-36,800
17,5
20,000-31,200
22
36,800-66,400
22,5
31,200-55,200
28
66,400 -
30
55,200-
35
15,600-23,200
6,5
11,700-14,500
11
23,200-37,800
17,5
14,500-20,200
15
37,800-68,200
22,5
20,200-31,500
21
68,200 -
30
31,500-55,800
27
55,800-
34
2009
2010
2011
Note: Finnish marks are converted to euros before 2002.
Table 1: Central government marginal income tax rates, 1999-2011
29
Marginal income tax rate schedule
.2
Marginal tax rate
.3
.4
.5
.6
Years 1999, 2005 and 2011
0
20000
40000
60000
Taxable income
1999
2011
80000
100000
2005
Note: Marginal tax rate includes central government income taxes, average municipal income taxes and average social
security contributions.
Figure 16: Nominal marginal tax rates (MTR) on earned income, years 1999, 2005 and
2011
Before 2008
Study subsidy months
Income limit
After 2008
Relative income loss at
Income limit
Relative income loss at
the margin if income
the margin if income
limit is exceeded
limit is exceeded
1
17,340
3.1%
22,550
2.5%
2
16,330
3.2%
21,190
2.7%
3
15,320
3.5%
19,930
2.9%
4
14,310
3.7%
18,620
3.1%
5
13,300
4.0%
17,310
3.3%
6
12,290
4.3%
16,000
3.6%
7
11,280
4.7%
14,690
3.9%
8
10,270
5.2%
13,380
4.3%
9
9,260
5.7%
12,070
4.8%
Note: The relative loss from marginally exceeding the income limit is calculated using the full study subsidy (461 euros
and 500 euros before and after 2008, respectively) plus 15% interest collected by the Social Insurance Institution.
Table 2: Income limits in the study subsidy system and the relative marginal loss if the
income limit is exceeded (in proportion to gross income at the limit), before and after
the reform of 2008 (academic years 2006/2007 and 2008/2009, respectively)
30
Variable
N
Mean
Std. Dev.
Taxable earned income
45,494,860
22,981
31,048.75
Gross earned income
45,494,615
25,520
31,986.62
Taxable capital income
45,494,860
1,803
50,947.13
Age
45,494,860
43.06
14.816
Female
45,494,860
0.498
.50
Size of the household
44,963,949
2.68
1.438
Table 3: Summary statistics, all taxpayers, 1999-2011
All students
N
Mean
Std. Dev.
Taxable income
3,970,775
6,115
5,072.32
Gross income (subject to income limit)
2,711,754
7,614
8,619.77
Age
3,980,502
23.30
5.093
Subsidy months
3,255,567
7.15
2.762
Income limit
3,249,902
11,730
3,206.64
Students with 9 months of study subsidy
N
Mean
SD
1,163,189
5,024
3,879.44
708,525
5,587
6,492.77
Age
1,163,617
22.54
4.486
Subsidy months
1,163,617
9
0
Income limit
1,163,189
9,770
1,083.15
Taxable income
Gross income (subject to income limit)
Table 4: Summary statistics, students, 1999-2010
Variable
N
Mean
Std. Dev.
Taxable earned income
3,351,466
25,601
26,860
Gross earned income
3,385,734
26,970
27,734.4
Capital income
2,236,182
7,096
561,620.2
Turnover (rm-level)
3445810
149,931
663,409.8
Net assets (rm-level)
2956521
15,211
217,001.8
No. of employees (rm-level)
2189383
.661
2.587
Table 5: Summary statistics, self-employed (sole proprietors and partners of partnership
rms), 1999-2011
31
Income distribution around the old notch before 2008, all students
1000
1500
Frequency
2000
2500
3000
Excess mass: .289 (.173),
-50
-40
-30
-20
-10
0
10
20
Distance from the notch
Observed
30
40
50
Counterfactual
Figure 17: Income distribution around the old income limit before the reform of 2008, all
students 2008-2010
Study subsidy notch, all students 1999-2001
Study subsidy notch, all students 2002-2004
Excess mass: 2.223 (.316), Share in the dominated region: .899 (.043)
Upper limit: 25 (5.029)
0
500
200
1000
Frequency
1500 2000
Frequency
400
600
2500
800
Excess mass: 1.515 (.643), Share in the dominated region: .943 (.098)
Upper limit: 25 (8.66)
-40
-30
-20
-10
0
10
20
Distance from the notch
Observed
30
40
50
-50
-40
-30
Counterfactual
-20
-10
0
10
20
Distance from the notch
Observed
30
Counterfactual
Study subsidy notch, all students 2005-2007
2000
Frequency
3000 4000
5000
6000
Excess mass: 2.503 (.383), Share in the dominated region: .932 (.059)
Upper limit: 26 (4.498)
1000
-50
-50
-40
-30
-20
-10
0
10
20
Distance from the notch
Observed
30
40
50
Counterfactual
Figure 18: Bunching at the study subsidy notch in dierent years
32
40
50